| Since the notion of rough set was originally proposed by Pawlak, it has been developed in practice quickly and has shown great superiority, especially in Knowledge discovery, Data mining etc. During the development of rough sets theory, scholars have paid great attention to constructing new rough model and investigating new theories by connecting the theory of rough sets with other theories, such as fuzzy sets, operator theory, evidence theory and so on.Comparing with Pawlak rough model, constructing a new rough model is carried out mainly from three aspects: universe, relation, and approximated sets. This thesis is based on T-fuzzy rough set and extend fuzzy set to L-fuzzy set, T- fuzzy similarly relation to TL-fuzzy similarly relation. Moreover, the triangular norm on a complete completely distributive lattice and conjunction operator are defined in the literature by extending interval [0,1] to complete completely distributive lattice, and the relation between which and the residual lattice is discussed. Based on the above theories, TL- fuzzy rough set is proposed, and the properties of the upper and lower approximation of L-fuzzy sets.We can induce the concept of the rough algebra, such as rough groups, rough ideals etc, by introducing the rough set to the crisp algebraic structure. In this thesis, based on the present literature the upper and lower approximations of a TL-fuzzy set are defined by introducing the theories of group to TL- fuzzy rough sets. We also discuss the approximation of the product of TL-fuzzy group and compound of TL-fuzzy relation in the thesis. In addition, the properties of the approximation of TL-fuzzy subgroup under the homomorphism are also investigated. At last, a theory describes the upper approximation of TL-fuzzy factor group. |
